Solve (-1/3x^{2}y)^{2}(5/4x)+(1/2x^2y)^4:(-9/20x^3y^2)

$$( - \frac { 1 } { 3 } x ^ { 2 } y ) ^ { 2 } ( \frac { 5 } { 4 } x ) + ( \frac { 1 } { 2 } x ^ { 2 } y ) ^ { 4 } : ( - \frac { 9 } { 20 } x ^ { 3 } y ^ { 2 } )$$

Evaluate

$$0$$

Solution Steps

Expand \left(-\frac{1}{3}x^{2}y\right)^{2}.

$$\left(-\frac{1}{3}\right)^{2}\left(x^{2}\right)^{2}y^{2}\times \frac{5}{4}x+\frac{\left(\frac{1}{2}x^{2}y\right)^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\left(-\frac{1}{3}\right)^{2}x^{4}y^{2}\times \frac{5}{4}x+\frac{\left(\frac{1}{2}x^{2}y\right)^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{9}x^{4}y^{2}\times \frac{5}{4}x+\frac{\left(\frac{1}{2}x^{2}y\right)^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

Multiply \frac{1}{9} and \frac{5}{4} to get \frac{5}{36}.

$$\frac{5}{36}x^{4}y^{2}x+\frac{\left(\frac{1}{2}x^{2}y\right)^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{5}{36}x^{5}y^{2}+\frac{\left(\frac{1}{2}x^{2}y\right)^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

Expand \left(\frac{1}{2}x^{2}y\right)^{4}.

$$\frac{5}{36}x^{5}y^{2}+\frac{\left(\frac{1}{2}\right)^{4}\left(x^{2}\right)^{4}y^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{5}{36}x^{5}y^{2}+\frac{\left(\frac{1}{2}\right)^{4}x^{8}y^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{5}{36}x^{5}y^{2}+\frac{\frac{1}{16}x^{8}y^{4}}{-\frac{9}{20}x^{3}y^{2}}$$

Cancel out y^{2}x^{3} in both numerator and denominator.

$$\frac{5}{36}x^{5}y^{2}+\frac{\frac{1}{16}y^{2}x^{5}}{-\frac{9}{20}}$$

Divide \frac{1}{16}y^{2}x^{5} by -\frac{9}{20} by multiplying \frac{1}{16}y^{2}x^{5} by the reciprocal of -\frac{9}{20}.

$$\frac{5}{36}x^{5}y^{2}+\frac{\frac{1}{16}y^{2}x^{5}\times 20}{-9}$$

Multiply \frac{1}{16} and 20 to get \frac{5}{4}.

$$\frac{5}{36}x^{5}y^{2}+\frac{\frac{5}{4}y^{2}x^{5}}{-9}$$

Divide \frac{5}{4}y^{2}x^{5} by -9 to get -\frac{5}{36}y^{2}x^{5}.

$$\frac{5}{36}x^{5}y^{2}-\frac{5}{36}y^{2}x^{5}$$

Combine \frac{5}{36}x^{5}y^{2} and -\frac{5}{36}y^{2}x^{5} to get 0.

$$0$$

Factor

$$0$$